4 2/6 - 3/n = 4 17/24
subtract 4 2/6 from each side
4 2/6 - 4 2/6 - 3/n = 4 17/24 - 4 2/6
-3/n = 4 17/24 - 4 2/6
get a common denominator for the right hand side (24)
-3/n = 4 17/24 - 4 2/6* 4/4
-3/n = 4 17/24 - 4 8/24
-3/n = 9/24
multiply by n on each side
-3/n * n = 9 * n /24
-3 = 9/24 * n
multiply by 24/9 on each side
-3 * 24/9 = 24/9 * 9/24 *n
-8 = n